14. (a) Use differentiation to find the first two non-zero terms of the Maclaurin expansion of \(\ln \left( \frac { 1 } { 2 } + \cos x \right)\).
(b) By considering the root of the equation \(\ln \left( \frac { 1 } { 2 } + \cos x \right) = 0\) deduce that \(\pi \approx 3 \sqrt { 3 \ln \left( \frac { 3 } { 2 } \right) }\).
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